Lunar distance
The instantaneous Earth–Moon distance, or distance to the Moon, is the distance from the center of Earth to the center of the Moon. Lunar distance (LD or ), or Earth–Moon characteristic distance, is a unit of measure in astronomy. More technically, it is the semi-major axis of the geocentric lunar orbit. The lunar distance is on average approximately 385,000 km (239,000 mi), or 1.28 light-seconds; this is roughly 30 times Earth's diameter or 9.5 times Earth's circumference. Around 389 lunar distances make up an AU astronomical unit (roughly the distance from Earth to the Sun).
For the navigation unit, see Lunar distance (navigation).
Lunar distance is commonly used to express the distance to near-Earth object encounters.[1] Lunar semi-major axis is an important astronomical datum; the few millimeter precision of the range measurements determines semi-major axis to a few decimeters; it has implications for testing gravitational theories such as general relativity,[2] and for refining other astronomical values, such as the mass,[3] radius,[4] and rotation of Earth.[5] The measurement is also useful in characterizing the lunar radius, as well as the mass of and distance to the Sun.
Millimeter-precision measurements of the lunar distance are made by measuring the time taken for laser beam light to travel between stations on Earth and retroreflectors placed on the Moon. The Moon is spiraling away from Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging experiment.[6][7][8]
Because of the influence of the Sun and other perturbations, the Moon does not travel on a true ellipse around the Earth. Different methods have been used to nevertheless define a semi-major axis. Ernest William Brown provided a formula for the parallax of the Moon as viewed from opposite sides of the Earth, involving trigonometric terms. This is equivalent to a formula for the inverse of the distance, and the average value of this is the inverse of 384,399 km (238,854 mi).[9][10] On the other hand, the time-averaged distance (rather than the inverse of the average inverse distance) between the centers of Earth and the Moon is 385,000.6 km (239,228.3 mi). One can also model the orbit as an ellipse that is constantly changing, and in this case one can find a formula for the semi-major axis, again involving trigonometric terms. The average value by this method is 383,397 km.[11]
The actual distance varies over the course of the orbit of the Moon. Values at closest approach (perigee) or at farthest (apogee) are rarer the more extreme they are. The graph at right shows the distribution of perigee and apogee over six thousand years.
Jean Meeus gives the following extreme values for 1500 BC to AD 8000:[12]